Mathematics and Statistics

Department

Knowledge Book
GCSE Statistics
Term 10.1
Data Collection Scan here
for

Name: ______________________
 Teacher:
______________________

2|Page
3|Page
 Contents Page
What is ‘data’ and how can we collect
it?

Page

*How can we identify if data is Primary or Secondary? 6

*How can we identify if data is Qualitative or 10

Quantitative?
How can we identify if data is Categorical, Ranked or 14
Bivariate?
How can we write an appropriate hypothesis for an 17
investigation?
How do we identify the population needed for an 2
investigation?
*What are the pros and cons to taking a census? 23

How do we identify a sample, sample units and sample 25

frame?
How do we determine whether data given to us is a 30
parameter or a statistic?
*How can we explain how to take a random sample? 32

*How do we calculate and explain how to take a stratified 37

sample?
How do we calculate and explain how to take a 45
systematic sample?
How can we identify the sampling method from a written 49
scenario?
What are the advantages and disadvantages of the 53
various sampling methods?
*How can we use the capture/recapture method for 57
estimating population sizes?
*How do we ensure that a questionnaire is useful, 61
practical and suitable for an investigation?
How and why do we ‘clean’ data? 68

4|Page
Cross-Curricular
Link All small questions marked with a * are topics that you will
be coving in GCSE Maths as well as GCSE Statistics

Vocabulary Pyramid

Sample
Census
Sample_Un
Tier 3 Words its
Words specific to the subject ‘Statistics’
Sample_Fra
These may have different meanings me in
other subjects Discrete
Continuous
Primary
Secondary
Qualitative
Quantitativ
e
Categorical
Tier 2 Words Ranked
Data Identify Describe Discuss
Words that are often seen Variables Determine Parameter Statistic
written in text and exam
questions but are not Evaluate Respectively Given Explain Conduct
often spoken
Suggest Assess Validity Research Investigate
Calculate Practical Suitable Collect
Tier 1 Words
Words that are
used often in
Who What Where When Why How
speech and
have the same Age Time Weight Mass Length Breadth Width Height
meaning in
most Cheap Expensive Quick Time_Consuming
contexts Advantages Disadvantages

5|Page
In this Knowledge Book you will see some of the following symbols with interesting
facts and information about the words and terminology which will not be assessed but
will deepen your understanding of the words.

This gives us the origin of a word and the historical

development of its meaning.

This gives us a word or phrase that means exactly or nearly

the same as another word or phrase in the same language.

Historical
Origins Historical Origins. This gives us the historical origin of the
word.

Did you know?

Do you Know? This gives us a fascinating fact about the
word or skill,

Cross-Curricular
Link Cross Curricular Link. This gives us links to where we might
use this word or skill in other subjects

Real World
Application Real World Application. This gives us an idea of when or
how we might use this in the real world.

Revision Ideas Revision ideas. This gives us some revision techniques to

use for each topic.
Remember to use the revision websites:
 MrsHodgettsStatistics.com
 StatsAcademy.co.uk
 MathsGenie.co.uk
And the Revision techniques websites:
 GetRevising.co.uk
6|Page
 ______ / ______ / ______
Primary and Secondary Data
What is ‘data’ and how can we collect
it?

*How can we identify if data is Primary or

Secondary?
Key Vocabulary

Vocab Mathematical Definition

data which you collect yourself or is collected by your team

Primary Data
specifically for the investigation in hand

data which has already been collected or already exists but

Secondary Data
can be used for the investigation in hand

The Knowledge Phase

Primary Data – data which you collect yourself or is collected by your team
specifically for the investigation in hand
Examples:
- _____________________________________________________________
- _____________________________________________________________
- _____________________________________________________________
Advantages Disadvantages
✓ The collection method is known x Time consuming
✓ The accuracy is known x Expensive
✓ The questions can be tailored to the
investigation
Secondary Data – data which has already been collected or already exists but can
be used for the investigation in hand
Examples:
- _____________________________________________________________
- _____________________________________________________________
- _____________________________________________________________
Advantages Disadvantages
✓ Cheap x May be out of date
✓ Quicker than Primary x May have mistakes
✓ Can be more accurate if from a x May not answer the investigation
reliable source properly

7|Page
Did you know? You may have come across the words primary and
secondary in terms of the schools that you went to
You may have come across the terms primary and
secondary sources in History or English

Cross-Curricular
Link You may use primary and secondary data when collecting
information in Science or Geography

I DO

If I were to collect the annual household income

of a sample of 100 houses from the online
version of the 2020 UK Census. What sort of
data would this be?

WE DO

What sort of data is being collected by Sam who

is measuring the amount of rain collected in a
bottle outside the classroom every 30 minutes?

YOU DO

Scott is researching opinions on the uniform at

his school. He asks a sample of pupils whether
they believe the uniform should be changes.
Will his data be Primary or Secondary?

8|Page
 Practice Questions
1. For each of the following, select if the data would be primary or secondary:
(a) Richard wants to know his friends’ favourite colour.
He asks his 10 friends their favourite colour. Primary /
Secondary
(b) Laura wants to know how many cars travel down her street between 9am and
10am.
She stands outside her house and records how many cars drive down her street.
Primary / Secondary
(c) Hollie wants to know how many people live in her village.
She looks it up on the internet. Primary /
Secondary
(d) Joseph wants to find out if students like school dinners in his school
He carries out a survey Primary / Secondary
(e) Kyle collects information from the internet the weather in April over the last 10
years.
Primary / Secondary
(f) Erin wants to find out information about the life expectancy of penguins
She watches a documentary on penguins to find out Primary /
Secondary
(g) Rosie wants to find out the mass of an orange
She weighs 5 oranges Primary /
Secondary
(h) Neil wants to find out information about how often people visit the cinema and
how much money they spend while they’re there

Neil asks people to fill out a questionnaire Primary /

Secondary

2. For each of the following data collection methods, shade in any examples of
Primary data and leave the examples of secondary data unshaded

Ahmed is writing down the Belinda is writing down the

Caleb is watching students
football results from past colour of cars which go
enter the canteen at break
Saturdays premier league past her as she sits on the
on CCTV and recording it
matches to draw a bar wall outside to do a
in a tally chart for a
chart for the number of pictogram of common car
project on healthy eating
goals scored colours

Daisy is using the internet Elvis was away for last Grace is in the playground
to find out how many weeks science experiment asking fellow students to
students there are in each and is copying Frank’s answer 3 questions about
year group in results to use for his own break time as she wants to
Wolverhampton schools to get it extended by 10
9|Page
 calculate average class
analysis minutes
sizes

Hamza was reading the Jaxson is recording the

house prices in the time it takes to get from
Isla is reading her
newspaper to calculate an each lesson to the next in
favourite book and notes
estimate of how much he order to report to the
the page number every
needed to start saving in head-teacher on how
time she finds her name
order to get on the many wasted minutes he
property ladder has each week

Exam Questions
1. A drug company wants to find out how effective a new drug is at relieving pain.
The drug is to be tested on different age groups.
The company decides to take a stratified sample of the patient results from
Skipworth Clinic who have been taking recordings of the levels of pain felt by
patients using the drug.
What type of data will the company collect?
(1 mark)

2. The BabyDrive company is designing a car seat for babies. The company has to
decide what size to make the seat. The company asks for data about the babies
born in five UK hospitals in the last year. The company does this by carrying out
a survey.
(b) (i) State whether the data in the survey is primary or secondary. Give a
reason for your answer.
(1 mark)
(ii) Give one advantage and one disadvantage of using this type of data.
(3 marks)

3. The owner of a bakery wants to open a new store in a large town. He wants to
find out where the residents of the town want the store to be located.
(a) The owner of the bakery may have to use primary data. Give a reason why.
(1 mark)

4. Supul is investigating how long pupils in Year 10 in his school spent on

homework. He asked each pupil to record the time taken, to the nearest minute,
to do their homework one night. *(a) Describe the type of data the pupils
recorded.
(2 marks)
Supul collected each pupil’s recorded time. *(b) Discuss how reliable the data
might be
(2 marks)

5. Amy owns a cycle shop. She wants to find out information about cyclists in her
town. Amy plans to use primary data. (a) Give one advantage of using primary
data
(1 mark)

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 6. Estelle is the manager of a company with 50 employees. She is going to give a
questionnaire to each employee to get information about the food served in the
company’s canteen.
Estelle will be collecting primary data.
(b) (i) Explain what is meant by primary data.
(1 mark))
(ii) Give one advantage of using primary data.
(1 mark))

Create flash cards with lots of different examples of primary and

secondary data to test yourself with. Try using GetRevising.co.uk

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 ______ / ______ / ______
Qualitative and Quantitative Data
What is ‘data’ and how can we collect
it?

*How can we identify if data is Qualitative or

Quantitative?
Key Vocabulary
Vocab Mathematical Definition
Qualitative Data data which is non-numerical
data which is numerical. This can be split into two sub-
Quantitative Data
categories
Discrete Data numerical data which is countable

Continuous Data numerical data which is measurable

Qualitative: Latin ‘qualitas’ and the English ‘quality’

Quantitative: Latin ‘quantitas’ and the English ‘quality’
Discrete: Latin ‘discretus’ meaning to separate
Continuous: Latin ‘continuus’ meaning uninterrupted

The Knowledge Phase

Qualitative Data – data which is non-numerical
Examples:
- _____________________________________________________________
- _____________________________________________________________
- _____________________________________________________________

Quantitative Data - data which is numerical. This can be split into two sub-
categories
Discrete Data – numerical data which - _________________________________
is countable - _________________________________
- _________________________________
Examples:

Continuous Data – numerical data - _________________________________

which is measurable - _________________________________
- _________________________________
Examples:

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I DO

Is the average amount of money spent Qualitative

or Quantitative?

WE DO

Is currency discrete or continuous data?

YOU DO

Is time taken to complete a marathon

discrete or continuous data?

Practice Questions
1. Emily is doing a survey on the colours of cars. She is going to count the number of
cars of each colour in a car park. Decide if the following data is qualitative or
quantitative
(a) The number of cars Qualitative /
Quantitative
(b) The colour of the cars Qualitative /
Quantitative
2. Eddie carries out a survey about the pet dogs his classmates own. Decide if the
following data is qualitative or quantitative
(a) How many dogs each person owns Qualitative /
Quantitative
(b) The type of dog Qualitative /
Quantitative
(c) The name of each dog Qualitative /
Quantitative
(d) The age of each dog Qualitative /
Quantitative
(e) The mass of each dog Qualitative /
Quantitative
3. Max is writing a report about the Statue of Liberty
(a) List 4 quantitative variables that Max could include in his report

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1. __________________________________ 2.
__________________________________
3. __________________________________ 4.
__________________________________
(b) List 4 qualitative variables that Max could include in his report
1. __________________________________ 2.
__________________________________
3. __________________________________ 4.
__________________________________
4. For each of the following, state if the data would be discrete or continuous:
(a) The number of people in a room
Discrete / Continuous
(b) The mass of a book Discrete /
Continuous
(c) The number of pages in a book Discrete /
Continuous
(d) The length of a line Discrete /
Continuous
(e) The time taken to complete a puzzle Discrete /
Continuous
(f) The size of a shoe Discrete /
Continuous
(g) The number of glasses in a dishwasher
Discrete / Continuous
(h) The volume of water in a bottle Discrete /
Continuous
(i) The number of songs in an album
Discrete / Continuous
(j) The weight of an apple Discrete /
Continuous
(k) The number of people at a football match Discrete /
Continuous
5. A teacher collects the ages of students in her school. Is that variable discrete or
continuous?
Discrete /
Continuous
6. Steven keeps a record of the prices of all the cars he sold in one year. Is that
variable discrete or continuous?
Discrete / Continuous

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7. Is money discrete or continuous? Explain your answer.
Discrete / Continuous
_______________________________________________________________________________________
_______________________________________________________________________________________
_______________________________________________________________________________________
8. Is the value of an antique discrete or continuous?
Discrete / Continuous
9. For each of the following types of data, colour code those which are Qualitative,
Continuous and Discrete

The length of the

The colour of the The number of The age of the
girls hair in
cars in the car park pupils in year 11 pupils in year 7
Emerald house

The height of the The sex of the

The weights of the The cost of a new
teachers at students taking
pupils bags in KS3 set of text books
Aldersley GCSE Statistics

The width of the The names of the

The nationality of The shoe size of
gaps between the players on the
the MFL teachers the LSA staff
exam tables football team

Create flash cards with lots of different examples of qualitative, discrete

and continuous data to test yourself with. Try using GetRevising.co.uk

Exam Questions
1. A car salesman records information about the cars he is selling. Here is a list of words

Qualitative Continuous Discrete

Use a word from the list to complete each sentence.

(a) The number of doors is .................................... data. (1 mark)

(b) The age of each car is .................................... data. (1 mark)

(c) The colour of the car is .................................... data. (1 mark)

2. A shop owner records information about his customers.

Put a cross in the box to indicate whether each of the following is qualitative or quantitative data.

(a) The distance travelled to get to the shop

Qualitative  Quantitative  (1 mark)

(b) The method of transport

Qualitative  Quantitative  (1 mark)

3. A car repair garage records information about the cars it repairs.

Put a cross in the box to indicate whether each of the following is discrete or continuous data.

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(a) The length

Discrete  Continuous  (1
mark)

(b) The time taken to repair each car

Discrete  Continuous  (1
mark)

(c) The number of seats

Discrete  Continuous  (1
mark)

(d) The number of gears

Discrete  Continuous  (1
mark)

(e) The number of miles per gallon

Discrete  Continuous  (1
mark)

4. There are 40 sheep on a farm. Use the best word from the list to complete each sentence below.

Qualitative Continuous Discrete

(a) The colours of the sheep are ................................ data (1 mark)

(b) The weights of the sheep are ................................ data (1 mark)

5. Robert says he is 13 years old. Alan says Robertʼs response is continuous data. Hannah says Robertʼs response is
discrete data. Who do you agree with? Explain your
answer. ......................................................................................................................................................................

......................................................................................................................................................................

...................................................................................................................................................................... (1 mark)

______ / ______ / ______

Categorical, Ranked and Bivariate Data
What is ‘data’ and how can we collect
it?

How can we identify if data is Categorical,

Ranked or Bivariate?
Key Vocabulary
Vocab Mathematical Definition
A set of data is categorical if values or observations
Categorical Data
belonging to it can be sorted into different categories
Values that can be ranked or have a rating
Ranked Data scale attached. It can be counted and ordered but NOT
measured
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 Bivariate Data Pairs of related variables

The Knowledge Phase

Categorical Data – A set of data is categorical if values or observations belonging
to it can be sorted into different categories
*Categorical Data can be both Qualitative or Quantitative*
Examples:
- _____________________________________________________________
- _____________________________________________________________
- _____________________________________________________________

Ranked Data – Values that can be ranked or have a rating

scale attached. It can be counted and ordered but NOT measured
*Ranked Data can be both Qualitative or Quantitative*
Examples:
- _____________________________________________________________
- _____________________________________________________________
- _____________________________________________________________

Bivariate Data – Pairs of related variables

*Bivariate Data can only be Quantitative*
Examples:
- _____________________________________________________________
- _____________________________________________________________
- _____________________________________________________________

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I DO

The year group a student is in

Would this data be categorical, ranked or
bivariate?

WE DO

The age and heights of the students

Would this data be categorical, ranked or
bivariate?

YOU DO

The league positions of football teams

Would this data be categorical, ranked or
bivariate?

Practice Questions
1. For each of the following scenarios, decide which type of data best describes it;
categorical, ranked or bivariate.
(a) The number of sales sold at different temperatures Categorical /
Ranked / Bivariate

(b) The colour of a ball in the P.E cupboard Categorical /

Ranked / Bivariate

(c) The number of traffic accidents on a stretch of road with the volume of rain each
day
Categorical / Ranked /
Bivariate

(d) The order in which pupils came in the 100m race Categorical /
Ranked / Bivariate

(e) The breed of a dog at crufts Categorical / Ranked

/ Bivariate

(f) The rating from 'very dissatisfied' to 'very satisfied' on an anonymous

questionnaire
Categorical / Ranked /
Bivariate
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2. Categorical Data
Suggest 3 categories to satisfy the following collected data:
(a) The size of the wheels of the student’s bikes
 _______________________  _______________________  _______________________
(b) The age of people taking their driving test

 _______________________  _______________________  _______________________

(c) The distance commuters travel to work
 _______________________  _______________________  _______________________

(d) The colour of the employees shoes

 _______________________  _______________________  _______________________

(e) The time taken to complete a crossword

 _______________________  _______________________  _______________________

3. Ranked Data
Rank these data in order from smallest to biggest
(a) 50 60 20 40 70 80 10
___ ___ ___ ___ ___ ___ ___
(b) 0.9 1.4 0.2 1.8 1.7 0.6
___ ___ ___ ___ ___ ___
(c) 24 31 26 29 35 34 20 30 37
___ ___ ___ ___ ___ ___ ___ ___ ___
(d) 164 122 153 161 147 158 129 135
___ ___ ___ ___ ___ ___ ___ ___
(e) G A B D E F C
___ ___ ___ ___ ___ ___ ___

4. Bivariate Data
Suggest what could be paired with each of the following data sets:
(a) Height and _________________________________________ of teachers
(b) GCSE Maths grade and ______________________________ of students
(c) Time spent revising for exams and _______________________________
(d) The number of Lego bricks used and the __________________________ of the structure
(e) Temperature outside and the number of ______________________ sold
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 Create a crossword or quizsearch for all of the key terms we have
covered so far to help you remember which is which. Try using
GetRevising.co.uk

20 | P a g e
 ______ / ______ / ______
Hypotheses
What is ‘data’ and how can we collect
it?

How can we write an appropriate hypothesis

for an investigation?
Key Vocabulary

Vocab Mathematical Definition

a sensible assumption written as a statement that can be

Hypothesis
tested to see if it is correct or not

Hypotheses: Greek ‘hupo’ and ‘thesis’ meaning under

placing

The Knowledge Phase

A hypothesis is a sensible assumption made as a starting point for an investigation.
This can then be tested using a variety of statistical techniques to see if it is correct or
not. Hence, it may or may not be true.
Some things we need to remember when writing a hypothesis …
 A hypothesis is not a question
 A hypothesis should be a statement
 A hypothesis should suggest a testable answer to the question
 A hypothesis should relate to as many aspects of the scenario as possible

How to start a hypothesis …

 The most popular / most common / most frequent … is …
 The average … is …
 There is a
a. weak / moderate / strong / very strong
b. positive / negative relationship between … and …
 … do better on average than …

And remember …
 If you are writing a hypothesis about averages include a time frame. E.G. The
average cost PER HOUR / PER DAY / PER WEEK / PER MONTH / PER YEAR
 Your hypothesis must be testable. i.e. do not write a hypothesis about
something you cannot measure or get the information for – be specific NOT
vague

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 Cross-Curricular You will have to use hypotheses in science when making
Link predictions about what results you will get form your
experiments

I DO

Ellis works in a tortilla chip factory and

has been asked to investigate the
average number of chips that are
deposited into each bag by machine D.
Suggest a suitable hypothesis for Ellis to
investigate.

WE DO

Tanzeen wants to investigate the

relationship between the number of
purple and green sweets in a quality
street tub.
Write down a suitable hypothesis for
Tanzeen to test.

YOU DO

Simon works on a chilli farm and in

interested in investigating the heat of the
various shades of chilli.
Suggest a suitable hypothesis for Simon
to use to for his investigation.

Practice Questions
1. For each of the following questions, decide if they are an example of a hypothesis
or not
a. Girls perform better, on average, than boys in GCSE Dance
b. I think the most common colour car is White
c. What is the correlation between the hand span and foot length of 24yr old
males?
d. The average number of cards made per hour is 540
e. The most popular flavour of crisps is Salt and Vinegar
f. What is the average time taken to complete a jigsaw?
g. I predict there will be a strong positive correlation between the weight and cost
of a parcel
h. There is a strong negative correlation between the force applied and the
number of upright pins
i. Which year group receives the most points?
j. The most frequent bird seen in the gardens is the pigeon

2. For each of the following studies, give an example of a hypothesis you could
investigate.
a. Benny wants to look at the number of words in the sentences, paragraphs and
chapters of books
22 | P a g e
 b. Daisy is interested in peoples preferred types of holiday and holiday destination
c. Freddie has a list of the retirement ages across all of the different countries in
Europe
d. Harriet wants to weigh all the different iPhones
e. Jack has a spreadsheet with the lengths and numbers of beats per minute of
different pieces of music
f. Lauren is investigating the time taken to read page 1 of 'Harry Potter and the
Prisoner of Azkhaban'
g. Neil is looking into the costs of holidays in the UK and those abroad for the
October half term
h. Pippa has asked her class to all estimate the weight of her calculator to the
nearest g
i. Richard has done an online search for the number of job vacancies in the
various counties in the UK
j. Tilly wants to know the sales figures for the last 10 years for her new favorite
band 'Fall Out Boy'

Exam Questions
1. Ron wants to investigate the average summer temperature in European cities.
He thinks this will be affected by the height of the city above sea level. He
writes down two statements.
Statement A: Do cities which are higher above sea level have a lower summer
temperature? Statement B: The higher the city is above sea level the lower the
summer temperature is.
(a) Statement A is not a hypothesis. Explain why.
(1 mark)
2. Aneena wants to investigate whether the boys at her school do more exercise
than the girls at her school. Suggest a hypothesis Aneena could use
(1 mark)
3. A table shows information about ten films that each won the Best Picture Oscar
award. Norman is investigating whether there is a relationship between the
runtime of a film and the USA Box Office takings. Write down a suitable
hypothesis for this investigation.
(1 mark)
4. A librarian wants to investigate, for books in her library, if there is a relationship
between how old a book is and for how long it is borrowed. (a) Suggest a
hypothesis that the librarian could use.
(1 mark)
5. Seb thinks that the number of medals won by a country in the Olympic Games is
affected by the wealth of the country. Suggest a hypothesis you could use to
investigate this.
(1 mark)
6. Jean is investigating if students at her college buy more ebooks downloaded
from the internet than books from shops. Write down a hypothesis that Jean
could use.
(1 mark)
7. A farmer is going to do an experiment to find out if using a new fertiliser will
produce more wheat. Write down a hypothesis he could use.
(1 mark)

23 | P a g e
 8. A researcher is investigating how safe residents of different ages feel in their
community at different times of the day. Suggest a hypothesis the researcher
can use.
(1 mark)
9. Zoe thinks the cost of a concert ticket depends on how long the concert lasts.
She investigates this for a sample of concerts during one year. (a) Write down a
hypothesis Zoe can use.
(1 mark)
10. Ruchi is investigating the relationship between an athlete's height and the
time the athlete takes to run 100 metres. Suggest a hypothesis she could use to
investigate this.
(1 mark)
11. Julie was investigating the relationship between the marks gained by
students in their GCSE Mathematics exam and the marks gained by the same
students in an A-level Mathematics exam. Suggest a hypothesis Julie could use.
(1 mark)

24 | P a g e
 ______ / ______ / ______
Population
What is ‘data’ and how can we collect
it?

How do we identify the population needed

for an investigation?
Key Vocabulary
Vocab Mathematical Definition
Everything or everybody that could possibly be involved in an
Population
investigation
Census Data collected from the whole population

Population: Latin ‘populus’ meaning people

Census: Latin ‘censere’ meaning to assess

The Knowledge Phase

Population - everything or everybody that could possibly be involved in an
investigation.
- This does not have to be the 'population' of Britain or the world
- The definition of ‘population’ can vary — for example it could be a class
group or the cars in a car park.
**REMEMBER** to use the phrase ‘all of the’ when describing the population
Sometimes, the population is small and easy to collect data from.
Other times the population is too large to handle or impossible to list and therefore a
sample (see page 15+) is used to collect the data

I DO

For the following investigation, state the

population that is to be considered:
What do pupils of Aldersley think of the
school dinners?

WE DO

For the following investigation, state the

population that is to be considered:
How long is a blade of grass?

25 | P a g e
YOU DO

For the following investigation, state the

population that is to be considered:
How heavy is the average donation bag
left at the Hammersmith Charity shop?

Cross-Curricular
Link You will look at various populations in Geography,
particularly populations of different countries.

Practice Questions
1. For each of the following investigations, state the population that is to be
considered
a. What do residents of Wolverhampton think about the current recycling
programme?
b. What proportion of the UK live on their own?
c. What to the employees of Kmart ltd think of the new management
structure?
d. What are the different blood types found in the donations made at the
Town Hall?
e. How many defects are found in a packet of Runners Crisps?

2. For each of the scenarios below, select the option which would be considered as
the appropriate
‘population’
a. Investigating year 9 students GCSE options at your school
 All of the year 9 students at your school
 Year 9 students at your school
 All of the students at your school
b. Investigating the number of chicken pieces in a factory-made Tikka
Masala
 All of the chicken in the factory
 All of the chicken Tikka Masala dishes from the factory
 Tikka Masala dishes from the factory
c. Investigating commuter times on the London underground
 Commuters using the London underground
 All of the commuters using the London underground
 All of the commuters in London
d. Investigating the viscosity of drinks from a work-placed vending machine
 All of the vending machines in the work place
 Drinks from a work-placed vending machine
 All of the drinks from a work-placed vending machine
e. Investigating local opinions of the postal service in the borough
 All of the opinions on the postal service
 Opinions in the local borough
 All of the people that live in the local borough
26 | P a g e
 3. Which of the following populations would be impossible to collect data from as a
whole?
a. All of the grains of sand on Talacre Beach
b. All of the pupils at Moreton High School
c. All of the water at Niagra Falls
d. Al of the people who live in Tettenhall
e. All of the televisions in the UK
Exam Questions
1. Julie’s school has been given Healthy School status. Julie wants to investigate if
students at her school now eat healthy meals.
State the population for her survey.
(1 mark)
2. Sandra owns a delivery company. She wants to investigate how satisfied
customers are with the company.
State the population for her investigation.
(1 mark)

3. A librarian wants to investigate, for books in her library, if there is a relationship

between how old a book is and for how long it is borrowed.
For the librarian’s investigation write down the population,
(1 mark)

4. There are 40 scouts in a scout group. The scout group leader needs to find out
the activities the scouts want to do at their summer camp. He is going to give a
questionnaire to all 40 scouts.
State the population.
(1 mark)

5. Percy is the conductor of a large choir. He is going to use a survey to find out
the type of music that people in the choir want to sing at the next concert.
State the population for his survey
(1 mark)

6. Julie and Bevan own a sandwich company. They deliver sandwiches to

customers for lunch in each of 30 offices every day. There are a number of
customers in each office. Julie wants to make changes to the sandwich menu.
She decides to find out the opinions of the customers. (a) Describe the
population for the survey.

27 | P a g e
 (1 mark)

______ / ______ / ______

Census
What is ‘data’ and how can we collect
it?

What are the pros and cons to taking a

census?
Key Vocabulary
Vocab Mathematical Definition
Everything or everybody that could possibly be involved in an
Population
investigation
Census Data collected from the whole population

Population: Latin ‘populus’ meaning people

Census: Latin ‘censere’ meaning to assess

The Knowledge Phase

A census is data collected from the whole population.
A census is:
✓ Unbiased x Time consuming
✓ Accurate x Expensive
✓ Takes every member of the x Can be a lot of data to handle
population into account x Can be difficult to ensure every
member of the population takes part

Did you know? The most well know example of a census is the UK National
census which is carried out every 10 years since 1801 by
the ONS.

Historical
Origins The UK census was first recorded in 1801

28 | P a g e
Exam Questions
1. Estelle is the manager of a company with 50 employees. She is going to give a
questionnaire to each employee to get information about the food served in the
company’s canteen. (a) Give one advantage of using a census rather than a
sample.
(1 mark)
2. Julie and Bevan own a sandwich company. They deliver sandwiches to
customers for lunch in each of 30 offices every day. There are a number of
customers in each office. Julie wants to make changes to the sandwich menu.
She decides to find out the opinions of the customers.
Bevan wants to use a census to collect the customers’ opinions.
(b) Write down one advantage of using a census.
(1 mark)
3. The head teacher wants to change the school starting time. She wants school to
start half an hour earlier. She wants to find out what the students think about
the change. She is going to ask a sample of students instead of using a census.
(a) Give two disadvantages of using a census.
(2 marks)
4. There are 40 scouts in a scout group. The scout group leader needs to find out
the activities the scouts want to do at their summer camp. He is going to give a
questionnaire to all 40 scouts
(b) Write down the statistical name for an investigation that gets information
from every member of the population.
(1 mark)

29 | P a g e
 ______ / ______ / ______
Sampling
What is ‘data’ and how can we collect
it?

How do we identify a sample, sample units

and sample frame?
Key Vocabulary

Vocab Mathematical Definition

Sample A small proportion of the population

Sample Units The people or things being sampled

Sample Frame A list of the population from which the sample can be obtained

The Knowledge Phase

A Sample is a small proportion of the population
Samples can be collected in a variety of way (we will look into this further later in the
unit)
A sample contains information about part of the population as opposed to a census
which contains information about all of the population
The purpose of a sample is to provide information which can be used to infer
information about the population in a more convenient way
A sample:
✓ is quick x can be biased
✓ is cheap x can be influenced by outliers
✓ is more convenient x does not take every member of the
population into account

The Sample Units are the people or things being samples

The Sample Frame is a list of the population from which a sample can be obtained.
- An employee or student register
- An electoral roll
- An inventory list

**AMAZING FACT YOU SHOULD KNOW**

A statistically large sample is any sample that is ≥30

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 Historical Sampling is known to have been first used more than a
Origins century ago, in the year 1895. This paper describes how
sampling became an accepted scientific method. It
concentrates on the use of sampling in official statistics, i.e.
statistics that are collected by government agencies, and
are used for policy making and scientific research

I DO

Why would it be more sensible to take a

sample than a census of calculators in
the maths department to estimate how
many are faulty?
Explain your answer

What would be the sample units for this

investigation?

What would be the sample frame, if any,

for this investigation?

WE DO

Why would it be more sensible to take a

sample than a census of the mothers in
the WV4 postcode for a questionnaire
about the under 5 facilities in the area?
Explain your answer

What would be the sample units for this

investigation?

What would be the sample frame, if any,

for this investigation?

YOU DO

Why would it be more sensible to take a

sample than a census of History teachers
in the UK to see what their favourite
period from history is?
Explain your answer

31 | P a g e
 What would be the sample units for this
investigation?

What would be the sample frame, if any,

for this investigation?

Practice Questions
1. For each of the following scenarios, decide if it would be best to choose a
sample or census
a. Checking the burning time of a new candle being produced by a small
family run business
 Sample  Census
b. Asking teachers in the UK their opinion on homework
 Sample  Census
c. Testing tins of baked beans for taste, colour and consistency
 Sample  Census
d. Inspecting the fittings on a newly constructed set of scaffolding
 Sample  Census
e. Examining boxes of cereal for foreign objects before leaving the factory
 Sample  Census

2. For each of the following populations, state what the sample units would be
a. Population: All of the Students at West Brinx College
Sample Units: ______________________________________________
b. Population: All of the Houses on Higgleton Street
Sample Units: ______________________________________________
c. Population: All of the Babies born on 01.01.2020 at a UK hospital
Sample Units: ______________________________________________
d. Population: All of the jars of jam from a factory
Sample Units: ______________________________________________

3. At its Web site, the Gallup Poll publishes results of a new survey each day. Scroll
down to the end, and you’ll find a statement that includes words such as these:
‘Results are based on telephone interviews with 1,008 national adults, aged 18
and older, conducted April 2-5, 2007… In addition to sampling error, question

32 | P a g e
 wording and practical difficulties in conducting surveys can introduce error or
bias into the findings of public opinion polls.’
a. For this survey, identify the sample and the population of interest
b. Gallup performs its surveys by phoning land-line numbers generated at
random by a computer program. What is the sampling frame?
c. What problems, if any, would you be concerned about in matching the
sampling frame with the population?

Questions 4-10.
For the following reports about statistical studies, identify the following items (if
possible). If you can’t tell, then say so – this often happens when we read about
a survey.
a) The population
b) The sampling frame
c) The sample
4. Consumers Union asked all subscribers whether they had used alternative
medical treatments and, if so, whether they had benefited from them. For
almost all of the treatments, approximately 20% of those responding reported
cures or substantial improvement in their condition.
5. Researchers waited outside a bar they had randomly selected from a list of such
establishments. They stopped every 10th person who came out of the bar and
asked whether he or she thought drinking and driving was a serious problem.
6. Hoping to learn what issues may resonate with voters in the coming election,
the campaign director for a mayoral candidate selects one block from each
city’s election districts. Staff members go there and interview all the residents
they can find. AP Statistics
7. The EPA took soil samples at 16 locations near a former industrial waste dump
and checked each for evidence of toxic chemicals. They found no elevated
levels of any harmful substances.
8. State police set up a roadblock to estimate the percentage of cars with up-to-
date registration, insurance, and safety inspection stickers. They usually find
problems with about 10% of the cars they stop.
9. A company packaging snack foods maintains quality control by randomly
selecting 10 cases from each day’s production and weighing the bags. Then
they open one bag each from each case and inspect the contents.
33 | P a g e
 10. Dairy inspectors visit farms unannounced and take samples of the milk to
test for contamination. If the milk is found to contain dirt, antibiotics, or other
foreign matter, the milk will be destroyed and the farm re-inspected until purity
is restored.

Exam Questions
1. One member of parliament in the UK wants to investigate the ages of the
people living in her constituency. She suggests using the electoral register as a
sample frame for her investigation.
a. State one use of a sample frame in an investigation
(1 mark)
b. Assess the suitability of using the electoral register as a sample frame for
this investigation.
(2 marks)

2. Some people think that drinking cocoa before bedtime may help to reduce blood
pressure.
A university student is going to research this.
a. The student decides to collect information from students at his university.
The student decides to use a sample, not a census.
Write down two reasons why. (2
marks)
b. Describe a sampling frame that the student could use.
(1 mark)

3. Sandra owns a delivery company. She wants to investigate how satisfied

customers are with the company.
When customers buy something, they are asked to agree to their names being
added to the company database.
(b) Identify one possible problem with using the company database as a
sampling frame.
(1 mark)

4. A librarian wants to investigate, for books in her library, if there is a relationship

between how old a book is and for how long it is borrowed.
34 | P a g e
 (c) For the librarian’s investigation write down
(ii) a suitable sampling frame.
(1 mark)

5. There are 40 scouts in a scout group. The scout group leader needs to find out
the activities the scouts want to do at their summer camp. He is going to give a
questionnaire to all 40 scouts.
(c) Give one reason why using a sample of the scouts in the group is not
necessary.
(1 mark)

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 ______ / ______ / ______
Parameters and Statistics
What is ‘data’ and how can we collect
it?

How do we determine whether data given to

us is a parameter or a statistic?
Key Vocabulary
Vocab Mathematical Definition
Any numerical value which is calculated or known about the
Parameter
population
Any numerical value which is calculated or known about the
Statistic
sample

The Knowledge Phase

A Parameter is defined as any numerical value which is calculated or known about the
population
A Statistic is defined as any numerical value which is calculated or known about the
sample
I DO
Is the total weight of all the chocolate
bars sold at the corner shop, a
parameter or a statistic?

WE DO
Is the mean weight of every 30th box of
cereal that comes off the production line
at the factory a parameter or statistic?

YOU DO
Is the modal colour of a sample of 30
cars on a car park a parameter or a
statistic?

36 | P a g e
37 | P a g e
 Practice Questions

1. State whether each underlined number is a parameter or a statistic.

a. A carload of ball bearings has a mean diameter of 2.5003 cm. This is within
the specifications for acceptance of the lot by the purchaser. By chance, an
inspector chooses 100 bearings from the lot that have a mean diameter
2.5009 cm. Because this is outside the specified limits, the lot is mistakenly
rejected.
i. 2.5003 _______________________ ii. 2.5009 _______________________
b. A telemarketing firm in LA uses a device that dials residential telephone
numbers in that city at random. Of the first 100 numbers dialed, 48% are
unlisted. This is not surprising because 52% of all LA residential phones are
unlisted.
i. 48% _______________________ ii. 52% _______________________
c. A researcher carries out a randomized comparative experiment with young
rats to investigate the effects of a toxic compound in food. She feeds the
control group a normal diet. The experimental group receives a diet with
2500 parts per million of the toxic material. After 8 weeks, the mean weight
gain is 335 grams for the control group and 289 grams for the experimental
group.
i. 335 _______________________ ii. 289 _______________________
In problems 2-8, determine whether the measured value is a statistic or a
parameter.
2. 10. A recent survey of 200 college career centers reported that the average starting
salary for petroleum engineering majors is $83,121.

3. The 2182 students who accepted admission offers to Northwestern University in

2009 have an average SAT score of 1442.

4. The areas of the countries in Africa are measured and their average is calculated.

5. In a random check of a sample of retail stores, the Food and Drug Administration
found that 34% of the stores were not storing fish at the proper temperature.

6. The average speed of the cars at the Brickyard during a race was 198 mph.

38 | P a g e
 7. You randomly select 8 cars to watch at the Brickyard during a race. Their average
speed was 201 mph.

8. The average salary for 35 of a company’s 1200 accountants is $68,000

______ / ______ / ______

Random Sampling
What is ‘data’ and how can we collect
it?

How can we explain how to take a random

sample?
Key Vocabulary
Vocab Mathematical Definition
Everything or everybody that could possibly be involved in an
Population
investigation
Sampling A small proportion of the population
Something that happens without method or conscious
Random
decision.
A sampling method in which everyone or everything has an
Random Sampling
equal chance of being chosen

The Knowledge Phase

A random Sample is one where everyone and everything from the population has an
equal chance of being chosen.
A random sample is chosen without a conscious decision about what or who is
selected from the population
Random Numbers can be found in a variety of ways:
- Names in a hat
- Internet generators
- Computer programmes such as Excel
- Random Number Tables
- Ran# on the calculator
Ran# on the calculator
The Ran# button gives you a number between 0 and 0.99 to 3 decimal places
The RanInt# button given you an integer between two identified values (which can b
e manipulated as required)
I DO

39 | P a g e
 Find a random integer
between 0 and 50

WE DO

Find a random integer

(multiple of 5) between 0 and
500
YOU DO

Find a random integer

between 20 and 60

Practice Questions
1. Find 10 random integers between 0 and 40

2. Find 10 random integers between 100 and 500

3. Find 10 random integers (multiple of 0.5) between 10 and 20

4. Find 10 random integers (multiples of 10) between 0 and 100

5. Find 10 random integers (multiples of 2) between 0 and 50

40 | P a g e
41 | P a g e
The Knowledge Phase
In the exam, your instructions for how to take a random sample must be clear
1) Number the units from 1-n in the sampling frame
2) Choose a random number from a random number generator
3) Ignore any repeats and numbers > n
4) Continue until x numbers obtained and choose the corresponding units from the
population
I DO
1)
___________________________________________________________
_____________________________________________________________
2)
Explain how to take a ___________________________________________________________
random sample of 6 _____________________________________________________________
pupils from a class of 3)
32 ___________________________________________________________
_____________________________________________________________
4)
___________________________________________________________
_____________________________________________________________
WE DO
1)
___________________________________________________________
_____________________________________________________________
2)
Describe how to take ___________________________________________________________
a random sample of _____________________________________________________________
12 houses from a 3)
street of 149 ___________________________________________________________
_____________________________________________________________
4)
___________________________________________________________
_____________________________________________________________
YOU DO

Take a random 1)
42 | P a g e
 ___________________________________________________________
_____________________________________________________________
2)
___________________________________________________________
sample of 10 babies
_____________________________________________________________
from a hospital
3)
where 8435 babies
___________________________________________________________
were born
_____________________________________________________________
4)
___________________________________________________________
_____________________________________________________________
Activity
For each of the scenarios below, match its corresponding random sampling
instructions using colour coding and number the steps from 1 - 4
A music shop
owner receives 60
Geffrey is a farmer.
applicants for a job.
He has 480 cows. Explain how you Describe a method
He decides to take
Geffrey wants to could interview 10 of choosing a
a random sample
take a random employees random sample of
of 20% of the
sample of 20 cows. randomly from a 15 students from a
applicants to find
Describe a method company of 600 primary school of
out how many have
that Geffrey could employees 141 students
a degree. Describe
use
how this sample
could be chosen
Ignore repeated Use a random
Number the Choose the
numbers or number generator
applications from 1 corresponding
numbers greater to select 20
to 60 employees
than 141 numbers
Ignore repeated Use a random Ignore repeated
Choose the
numbers or number generator numbers or
corresponding
numbers greater to select10 numbers greater
applicants
than 480 numbers than 60
Use a random
Number the Choose the
Number the cows number generator
students from 1 to corresponding
from 1 to 480 to select 15
141 students
numbers
Ignore repeated Use a random
Number the Choose the
numbers or number generator
employees from 1 corresponding
numbers greater to select 12
to 600 cows
than 600 numbers

43 | P a g e
 Practice Questions
1. How can a random sample of 8 pages from a book with 794 pages in total be
taken?

2. Explain how to take a sample of 20 sheep from a field of 321 sheep

3. Describe how to take a sample of 12 blood donations which are to be taken from
the 82 donations made this morning

4. Take a sample of 20 club members from the 126 members who have paid their
membership for next year.

5. Give instructions as to how Jemima can take a sample of 10 of her parishioners

from the 32 who are on the tea and coffee rota.

Create a flip book with the four steps for random sampling to test
yourself.

Exam Questions
1. A market research company is going to take a national poll.
They want to find out what people think about the performance of different
makes of new cars.
The company thinks about using a telephone poll.
There are 10 000 names in the phone book of one of these towns.
Describe how the company could take a random sample of 100 people from this
book.
(3 marks)
2. Tom and Samira want to collect data on the numbers of hours students at their
school spend on homework. There are 1100 students at their school. Tom is
planning to use a random sample of 50 students.
a. Explain what is meant by a random sample.
(1 mark)
b. Describe how Tom could use random numbers to take a random sample of
the students at his school.
(3 marks)
3. Samira wrote a questionnaire to investigate mobile phone use by the students
at her school. She decided to select a simple random sample from the 850
students at her school.
a. Explain what is meant by 'random' in this case.
(1 mark)
b. State the population for Samira's investigation.
(1 mark)
Samira obtained a list of all the students at her school, numbered 001 to
850, to use as a sampling frame. Samira decided to select her sample
using random numbers generated by her calculator. Here are her first 16
random numbers.

44 | P a g e
 032 079 156 248 953 214 209 665 321 147 523 324 654
247 851 207
Terri says these 16 random numbers will not give Samira 16 students for
her sample.
c. Explain why Terri is correct. Give two reasons.
(2 marks)
Terri suggests that Samira should select her sample by writing all the
students' names on pieces of paper, then picking them from a box without
looking.
d. Comment on whether Terri's method is appropriate.
(2 marks)
4. Parker wants to take a random sample of people who live in his street.
a. Explain what is meant by a random sample.
(1 mark)
b. Describe a method Parker could use to take his random sample.
(3 marks)

5. Gianluca is a farmer. He has 480 cows. Gianluca wants to take a random sample
of 20 cows. Describe a method that Gianluca could use
(4 marks)

6. A school has 2000 students. Explain how you could obtain a random sample of
35 students from this school
(4 marks)
______ / ______ / ______
Stratified Sampling
What is ‘data’ and how can we collect
it?

How do we calculate and explain how to

take a stratified sample?
Key Vocabulary
Vocab Mathematical Definition
Everything or everybody that could possibly be involved in an
Population
investigation
Sampling A small proportion of the population
Strata A group or category which the population has be split into
A sampling method which ensure the sample taken is
Stratified Sampling
proportionate to the strata which makes up the population

The Knowledge Phase

Strata is the statistical name for the groups/categories a population is split into.

45 | P a g e
These could be, qualitative discrete or continuous groups such as, colour, nationality,
shoe size, total, height, length etc. Each group or category is known as a ‘strata’
When populations are split into strata it is common for them to be uneven in size and
by taking a random sample it could be that different strata are under or over
represented or not represented at all.
Stratified Sampling allows us to take a random sample that represents the population
accurately
It considered the proportion of the population which resides in each strata and
ensures that the same proportion is represented in the sample.
i.e. if, in a population of 400 laptops, 25% of them are blue and the rest are black; in a
sample of 40 laptops a stratified sample would ensure that 10 of them were blue and
the rest black

To calculate the number needed for each strata sample:

Strata Total
X Sample Size
Population Total

46 | P a g e
I DO
Make Number of Cars
Kia 120
Fiat 60
Ford 150
Toyota 180
Audi 30
a) How many cars were there in total?
b) In a sample of 54, how many cars should be sampled
from the make:
i) Kia?
ii) Fiat?
iii) Ford?
c) In a Stratified Sample, 6 were sampled from Audi.
How many were sampled altogether?

WE DO
County Number of
people
Derbyshire 65
Leicestershire 80
Lincolnshire 15
Nottinghamshire 50
Staffordshire 40
a) How many people lived in the 5 counties in total?
b) In a sample of 25, how many people should be sampled
from:
i) Leicestershire?
ii) Nottinghamshire?
iii) Staffordshire?
c) In a Stratified Sample, 8 people were sampled from
Staffordshire.
How many were sampled altogether?

YOU DO
Degree Number of
Students
Maths 146
Physics 95
Biology 154
Chemistry 70
Statistics 55
a) How many students were on one of the 5 degrees in
total?
b) In a sample of 104, how many students should be
sampled from:
47 | P a g e
 i) Physics?
ii) Chemistry?
iii) Statistics?
c) In a Stratified Sample, 6 people were sampled from
Statistics.
How many were sampled altogether?
Practice Questions
1. Employees at a company are given either the role of management, sales,
technical or production.
A sample of 30 staff members is to be taken, stratified by job role.
Calculate the number of staff to be taken from each strata
Managemen Productio
Department t Sales Technical n
Employees 18 217 131 234
Sample Size

2. Students at a secondary school are taught in year groups.

A sample of 100 students is to be taken, stratified by year group
Calculate the number of students to be taken from each strata
Year 7 8 9 10 11
Students 158 213 213 280 140
Sample Size

3. Children who attend a local health clinic to be weighed are categorised by their
sex (male or female) and their age,.
A stratified sample of 45 children is to be taken
Calculate the number of children to be taken from each strata
0-6 6-12 1-2 2-3 3-4
Age months months years years years
Girls 53 54 59 56 62
Boys 53 60 57 62 56

4. Debbie is carrying out a survey to see how much people spend on groceries.
She has the following information about which people shop at which
supermarket in her town.
Superma Sainsbur Tesco Aldi Waitrose M&S

48 | P a g e
 rket y’s
No of
6400 5100 4500 2000 1350
shoppers
She wants to conduct a stratified sample of 200 people, how many people
should she survey from each supermarket?

49 | P a g e
 5.
Year Number of
Students
7 70
8 88
9 62
10 104
11 126
a) How many students were in the school in total? ________
b) In a sample of 90, how many students should be sampled from:
i) Year 7? ________ iv) Year 10? ________
ii) Year 8? ________ v) Year 11? ________
iii) Year 9? ________
c) In a Stratified Sample, 12 students were sampled from Year 8.
How many were sampled altogether? ________

6.
Employment Number of
Workers
Finance 70
Education 481
Health 620
Manufacturing 341
Transport 48
a) How many workers were employed in total? ________
b) In a sample of 50, how many workers should be sampled from:
i) Finance? ________ iv) Manufacturing? ________
ii) Education? ________ v) Transport? ________
iii) Health? ________
c) In a Stratified Sample, 20 workers were sampled from Health.
How many were sampled altogether? _______

50 | P a g e
The Knowledge Phase
In the exam, your instructions for how to take a stratified sample must be clear
A) Calculate the number to be sampled for each strata
1) Number the units from 1-n in the first strata
2) Choose random numbers from a random number generator
3) Ignore any repeats and numbers > n
4) Continue until x numbers obtained and choose the corresponding units from the
strata
B) Repeat this for each strata

I DO
A)
__________________________________________________________
____________________________________________________________
1)
__________________________________________________________
____________________________________________________________
Using stratified
_
sampling, explain how
2)
to take a sample of 12
__________________________________________________________
students from the
____________________________________________________________
population below
_
3)
Year 7 8 9
__________________________________________________________
10 11
____________________________________________________________
Students 15 18 10
_
5 2
4)
__________________________________________________________
____________________________________________________________
_
B)
__________________________________________________________
WE DO
Describe how a A) __________________________________________________________
stratified sample of ____________________________________________________________
51 | P a g e
 20 houses could be
1) __________________________________________________________
taken from the
_____________________________________________________________
population below
2) __________________________________________________________
_____________________________________________________________
Street No of
3) __________________________________________________________
houses
_____________________________________________________________
High St 42
4) __________________________________________________________
West Rd 17
_____________________________________________________________
East Ave 23
B) __________________________________________________________
South Ln 38
YOU DO
Explain how you
could take a
representative A) __________________________________________________________
sample of 50 babies ____________________________________________________________
born at various 1) __________________________________________________________
hospitals across the _____________________________________________________________
region in 2018. 2) __________________________________________________________
Use the information _____________________________________________________________
given below to help 3) __________________________________________________________
you _____________________________________________________________
4) __________________________________________________________
Hospital _____________________________________________________________
Births B) __________________________________________________________
St Marks 234 ____________________________________________________________
Willow Tree 474
Queen Mary 912

Practice Questions
1. Give a description of how a stratified sample of 100 pages could be taken from
the Roald Dahl books shown below
Book Matilda The BFG Charlie and the Choc Factory
Pages 284 215 306

52 | P a g e
 2. This table shows information about the number of students in years 9, 10 and
11
Year 9 Year 10 Year 11
100 50 50
The headteacher is going to survey some of the students about the school
library.
Explain how to take a stratified sample of 40 students from year s9, 10 and 11

3. A vet treats 100 pets over 1 week.

Cats Dogs Rabbits
30 50 20
A stratified sample of 10 is required.
Describe how this could be done

4. The table shows information about the inhabitants of a village.

Age Population Size
0 – 20 70
21 – 40 80
41 – 60 40
Over 60 10
Henry wants to take a sample of 40, stratified by age.
How would he do this?

5. A forest ranger wants to do a survey to check the general health of the trees int
heir care.
These are:
Oak Beech Walnut Pine Spruce
60 48 12 96 24
They have enough time to survey 40 trees and they want to do a stratified
survey.
Write instructions for the ranger to use to take a sample stratified by type of
tree

53 | P a g e
 Make sure you have copied the strata formula onto your formula page at
the back on the KB
Create a flip book with the four steps for stratified sampling to test
yourself.

Exam Questions
1. The table gives information about the numbers of students from different types
of schools who applied to Cambridge University in 2016 Richard is going to take
a sample of 200 of these students stratified by gender.
a) Work out how many female students there should be in this sample.
(2 marks)
b) Describe a situation when it would not be appropriate to take a sample
stratified by gender.
(1 mark)
Richard could have used a different category for his stratified sample.
c) What is this different category?
(1 mark)
2. The table shows the number of students in each year in the mathematics
department of a university.
Year first second third Total
Number of students 90 78 72 240
Amanda wants to find out what the students think about the mathematics
department.
She decides to take a sample of 40 of these students, stratified by year.
a) Show that there should be 15 first year students in the sample.
(1 mark)
b) Describe how Amanda would carry out her stratified sample
54 | P a g e
 (2
marks)
(4 The table shows information about houses for sale in Oxford.
Number of Bedrooms 1 2 3 4 5 or more Total
Number of Houses 140 300 420 240 100 1200
The estate agent wants to investigate the prices of these houses.
She takes a stratified sample of 60 houses according to the number of
bedrooms.
a) Work out the number of houses in her sample for each number of bedrooms.
(3
marks)
b) Describe how to select the 60 houses in the sample.
(3 marks)

(5 There are 180 employees in a school.

The table shows the number of each type of employee in the school. (
Teachers Teaching Assistants Admin Other
94 16 41 29
a) A stratified sample of size 50 is required.
Calculate the number of each type of employee that should be chosen
(3 marks)
b) Describe a method to obtain a stratified sample of size 50 from the
employees in the school
(3
marks)

55 | P a g e
 ______ / ______ / ______
Systematic Sampling
What is ‘data’ and how can we collect
it?

How do we calculate and explain how to

take a systematic sample?
Key Vocabulary
Vocab Mathematical Definition
Everything or everybody that could possibly be involved in an
Population
investigation
Sampling A small proportion of the population
Systematic A sampling method which uses a system of a regular interval
Sampling to find the sample.
A calculated value which determines how often a sample unit
Regular Interval
should be selected from the sample

The Knowledge Phase

A Systematic Sample is a sampling method which uses a system of a regular interval
to find the sample.
After selecting a random starting point, we then calculate what is known as the
‘regular interval’ which determines how often we select a sample unit form the
population.
This ‘regular interval’ is not random and must be calculated using the population size
(or an estimate of it) and the sample size you are intending to create
When Taking a Systematic sample we must first be able to calculate the interval:
Population
Sample
I DO

A street in Halesowen has 280 houses.

What would the regular interval be for a
sample of 8 houses?

WE DO

A factory produces approximately 300

bolts per hour.
What would the regular interval be for a
sample of 20 bolts per hour?

YOU DO

A shop has approximately 217 customer

56 | P a g e
 per day
What would the regular interval be for a
sample of 30 customers?

Practice Questions
1. A shop in town has 910 products in stock
The shop wants to take a systematic sample to check the quality of the products
in the store.
What would the regular interval be for a sample of 10 products?

2. A factory conveyor has 950 sweets travelling along it each day

The company director has asked staff to take a systematic sample to make sure
that all products are to an acceptable standard
What would the regular interval be for a sample of 25 sweets?

3. A school has 900 pupils in it at the start of the year

The head teacher wants to take a systematic sample of 10 pupils to see what
their opinions are of the school canteen
What would the regular interval be for this sample of pupils?

4. A plantation has 960 trees under 5 years old.

The agriculturalist wants to take a systematic sample to check the trees are
growing as they should
What would the regular interval be for a sample of 25 trees?

5. There are 970 houses in a village

The village school wants to take a systematic sample of estimate the number of
pupils who will be attending next year.
What would the regular interval be for a sample of 10 houses?

6. A local clothing store has 910 dresses in stock

The shop wants to take a systematic sample of 20 dresses to check the quality
of the dresses in the store.
What would the regular interval be for this sample of dresses?

7. In a warehouse a conveyor belts runs 950 boxes each day

The warehouse manager has asked staff to take a systematic sample to make
sure that all boxes are packed to an acceptable standard
What would the regular interval be for a sample of 10 boxes?

8. The Mathematics department at a university has 900 pupils in it at the start of

the year
The Head Maths lecturer wants to take a systematic sample of students to see
what their opinions are of the university facilities
What would the regular interval be for a sample of 10% of students?

9. A local garden centre has rows upon rows of 960 bedding plants
The manager wants to take a systematic sample to check the plants are
suitable for sale
57 | P a g e
 What would the regular interval be for a sample of 5% of the plants?

10. A factory produces approximately 14000 bars of soap per day.

They want to take a sample of 1% of the soaps that they make today for quality
control.
What would the regular interval be for the sample?

58 | P a g e
The Knowledge Phase
In the exam, your instructions for how to take a random sample must be clear
A) Calculate the 'regular interval'
1) Number the subjects from 1 to n
2) Choose a random number using a random number generator
3) Choose the corresponding subject from the population as a starting point
B) Using the 'regular interval' calculate the subjects needed for your sample

I DO
A)
__________________________________________________________
____________________________________________________________
1)
__________________________________________________________
____________________________________________________________
_
Explain how you could
2)
choose a systematic
__________________________________________________________
sample of 10 students
____________________________________________________________
from a class list of 30
_
students
3)
__________________________________________________________
____________________________________________________________
_
B)
__________________________________________________________
____________________________________________________________

WE DO
Explain how you could A)
choose a systematic __________________________________________________________
sample of 50 boxes of ____________________________________________________________
cereal from a 1)
production line of __________________________________________________________
approximately 2000 ____________________________________________________________
59 | P a g e
 _
2)
__________________________________________________________
____________________________________________________________
_
3)
boxes per day
__________________________________________________________
____________________________________________________________
_
B)
__________________________________________________________
____________________________________________________________

60 | P a g e
YOU DO
A)
__________________________________________________________
____________________________________________________________
1)
__________________________________________________________
____________________________________________________________
Describe how to
_
choose a systematic
2)
sample of 12
__________________________________________________________
tubs of sweets from
____________________________________________________________
the shelves of 60 tubs
_
which have just been
3)
delivered.
__________________________________________________________
____________________________________________________________
_
B)
__________________________________________________________
____________________________________________________________

Practice Questions
1. Define how you would take a systematic sample of 10 customers entering the
cinema from an estimated 234 customers
2. Describe how a systematic sample of 50 books from a library of 4389 books can
be taken
3. Explain how to take a systematic sample of 10 crabs out of a total catch of 90,
caught off the coast of Cornwall for a quality control check
4. Write a set of instructions for how to take a systematic sample of 1% of the
2500 fireworks delivered ready for 5th November
5. Describe how to take a systematic sample of

Exam Questions
1. Mike owns a shop.
He wants to collect information about the types of games liked by people in his
town.
61 | P a g e
 Mike is planning to send a questionnaire to some of his customers.
He wants to select the customers by using systematic sampling.
Mike has a list of all of his 200 customers.
Explain how Mike can select a systematic sample of 20 people from his list of
customers.
(2 marks)

Create a flip book with the four steps for systematic sampling to test
yourself.

62 | P a g e
 ______ / ______ / ______
Other Sampling Methods
What is ‘data’ and how can we collect
it?

How can we identify the sampling method

from a written scenario?
Key Vocabulary

Vocab Mathematical Definition

Everything or everybody that could possibly be involved in an

Population
investigation

Sampling A small proportion of the population

A sampling method which groups data into categories and

Cluster Sampling with either takes a sample of one cluster or a sample from a
small group of clusters

A sampling method which includes categories of data to fit a

Quota Sampling
given quota

Convenience A sampling method which collects data in the most convenient

Sampling way to the investigator

The Knowledge Phase

As well as being able to write instructions for how to take a random, stratified and
systematic sample, you should be able to identify each of these from a written
scenario along with cluster sampling, convenience sampling and quota sampling,

Cluster Sampling
 we group people into 'clusters'
 we randomly select a small sample of clusters
 we then either sample everyone from each of the chosen clusters
OR take a further random sample from each of the chosen clusters
* BE CAREFUL* this reads very similarly to stratified sampling.

WTLF: whether they sample a proportionate amount from each group (Stratified
Sampling) or just a random sample from some of the groups (Cluster Sampling)

63 | P a g e
Convenience Sampling
 we sample the people that are most convenient for us to find

WTLF: the phrase ‘asked the first __ people’ or ‘sampled the first ___ items’

Quota Sampling
 we are told the criteria of the type of people to be samples (our 'quota')
 we take a convenience sample of these types of people
 this method is most often used by market researchers

WTLF: a set number from different groups that haven’t been calculated.

I DO

Sharni plans to ask 10 male teachers, 10

female teachers, 10 girl students and 10 boy
students to take part in her questionnaire on
the new school menu
What sort of sampling is this?

WE DO

Alistair splits his local village into 4 areas and

plans on asking everybody from one randomly
chosen area their opinions on the change to
the bus service.
What type of sampling method is this?

YOU DO

Tyreece stood outside the chip shop that they

had just opened and asked the first 30 people
that walked past their opinions on the window
displays.
What method of sampling is this an example
of?

64 | P a g e
 Practice Questions
For each of the following, decide what sampling method is being used
a) Jermain, the owner of a nationwide restaurant chain, asks the managers from a
random sample of four of his restaurants to attend a conference with him
b) Alexa takes a list of the 32 people in her class and randomly selects 8 of them
for student voice
c) Josh samples 12 red cars, 12 blue cars, 12 black cars and 12 silver cars
d) Peter samples every 30th box that comes off the conveyor belt
e) Lucy takes a sample of 13% male and 87% female shoppers which is
proportionate to the population
f) Colin asks his friends at lunchtime what their favourite football team is
g) Jason numbers all of the phone numbers in the phone book from 1-n and
randomly selects 100 of them to call
h) A random number generator is used to pick a number from 1-10. Then every 9 th
number is chosen after that
i) Take a list of all the people in the village and pick 50 people at random
j) Split the village into 3 different age categories and choose a proportionate
amount for each group
k) Use a random name generator to select 50 students from the school register
l) Choose 15 students from each of the 5 houses in Windsor
m) Randomly choose one year group from school and take a small sample from just
that year group
n) Ask 10 men, 10 women, 10 girls and 10 boys
o) Take a list of all the people in the village and choose every 200th person on the
list
p) From the school register, choose every 32nd student
q) Stand outside the corner shop and ask the first 50 people you see
r) Split the village into 4 areas and choose a sample of the people in one of those
areas

65 | P a g e
 Create flash cards with lots of different examples of various sampling
methods to test yourself with. Try using GetRevising.co.uk

Exam Questions
1. The owner of a bakery wants to open a new store in a large town.
He wants to find out where the residents of the town want the store to be located.
The owner is going to select a sample of the town’s residents.
The owner will choose between two sampling methods.
Method 1: Grouping the town into 8 geographical regions. Then selecting all of the
residents in two randomly selected regions.
Method 2: Grouping the town into 8 geographical regions. Then randomly
selecting residents from each region in proportion to the number of residents in
that region.
a) Write down the name of sampling Method 1 (1
mark)
b) Write down the name of sampling Method 2 (1
mark)

2. Hamish wants to take a sample of bus passengers. Hamish plans to take a

sample of 50 men and 50 women. Name this sampling method
(1 mark)

3. There are 11 727 students at a university.

Their nationality is classified as UK, EU or International.
The table shows information about the nationality of these students.
Nationality UK EU International Total
Number of Students 9393 979 1355 11 727
The manager of a book shop wants to carry out a survey into the books read by
the students at this university. She is going to take a sample of 600 of these
students. The manager plans to sample 200 UK students, 200 EU students and
200 International students.
Write down the name of this method of sampling
(1 mark)
66 | P a g e
 4. A large company has 60 offices in different towns. The directors of the company
want to find out the opinions of their employees on a planned change to working
hours. They decide to choose at random 10 offices and survey all the employees
in these offices
(b) Circle the word below that best describes this sampling method.
Random Quota Systematic Stratified
(1 mark)

67 | P a g e
 ______ / ______ / ______
Advantages and Disadvantages of Sampling Methods
What is ‘data’ and how can we collect
it?

What are the advantages and disadvantages

of the various sampling methods?
Key Vocabulary
Vocab Mathematical Definition
Sampling A small proportion of the population
A sampling method in which everyone or everything has an
Random Sampling
equal chance of being chosen
A sampling method which ensure the sample taken is
Stratified Sampling
proportionate to the strata which makes up the population
Systematic A sampling method which uses a system of a regular interval
Sampling to find the sample.
A sampling method which groups data into categories and
Cluster Sampling with either takes a sample of one cluster or a sample from a
small group of clusters

A sampling method which includes categories of data to fit a

Quota Sampling
given quota

Convenience A sampling method which collects data in the most convenient

Sampling way to the investigator

The Knowledge Phase

As well as being able to write instructions for how to take a variety of samples and
identifying which sample is being taken from a set of instructions, we must also know
the advantages and disadvantages of each sampling method to help us to decide
which one to use if different situations.

68 | P a g e
 Sampling
Advantage Disadvantages
Method
- May not be representative of
- Everyone or everything has an the whole population
Random equal chance of being chosen - May not be possible to
- Minimal bias number the whole
population
- Time Consuming / Expensive
- Is representative of the whole
- May not be possible to
Stratified population
number the whole
- Minimal bias
population
- Can be biased as the regular
- Quick / Cheap interval could be stopping
- Easy / Convenient certain members of the
Systematic - Suitable for populations which population from being
are a constant flow such as a chosen
production line - Not random once the first
number has been chosen
- Can be biased as it may not
- Quick / Cheap
represent the whole
Cluster - Easy / Convenient
population
- Not Random
- Quick / Cheap
- Prone to bias
- Easy / Convenient
Quota - Not Random
- Ensures you have the type of
sample you need
- Quick / Cheap - Can be biased
Convenience
- Easy / Convenient - Not Random

I DO

Hugh wants to find out what residents of

his local town think about the plans to
build a new leisure complex.
He takes a convenience sample by
standing outside the sports centre at
10am on a Monday morning and asks the
first 100 people that come past.
Discus the sampling method he has
chosen.

WE DO

69 | P a g e
 Lolli wants to investigate how much time
her peers spend on homework.
She clusters her peers into their tutor
groups from years 7-11 and randomly
selects 3 tutor groups. She then asks all
students from each of the chosen tutor
groups.
Give one advantage and one
disadvantage of using this method.
YOU DO

Mel is a market researcher for

Plummel.org.
She has been instructed to ask 20
mothers with children, 20 businessmen
and 50 O.A.P’s
Explain why this sampling method might
be considered biased.

Practice Questions

1. Sue wants ti find out what people think of the new speed bumps on a street of
200 houses. She selects the 3rd, 8th, 13th houses and so on
a. Name this sampling method
b. Explain one advantage and one disadvantage of this method

2. Ali Is a marketing assistant for a chocolate company. To find out what people
think of a new chocolate bar, he asks 60 women and 20 men.
a. Describe the sampling method
b. Give one advantage and one disadvantage of this method

3. Alex is carrying out a survey on the morning by a very busy road. About 80 cars
per minute pass the point where Ales is standing. He wants to record the licence
plate and the number of occupants in 50 cars.
a. Explain why systematic sampling may be easier for Alex than random
sampling
b. Work out how long Alex should allow to collect his data
Alex decides ti collect data for half an hour every four hours, starting at
8.30am and finishing at 5.00pm
c. Explain why this method of sampling might not be a good one

4. Anushka is a senior police officer.

70 | P a g e
 She wants tot investigate morale at the 48 police headquarters based all over
the UK. She knows that about 40 people work at each headquarters. She wants
to survey abut 200 people and ask them what they think of the current
situation. Anushka takes a random sample of people
a. Give one disadvantage of this method she has chosen
b. Describe an alternative sampling method that Anushka could use to
improve her survey.

Create a mind map of the different sampling methods, their process and
their advantages & disadvantages. Try using GetRevising.co.uk

Exam Questions
1. Suha is carrying out market research in the town centre. She has been asked to
interview a total of 60 people of different ages and genders, as shown in the table.
Age 18–30 years Age 31–55 years Age 56 years and over
Male 10 10 10
Female 10 10 10
(a) Write down the statistical name of this sampling method.
(1 mark)
(b) Give one advantage and one disadvantage of this sampling method.
(2 marks)

2. The owner of a bakery wants to open a new store in a large town.

He wants to find out where the residents of the town want the store to be located.
The owner will choose between two sampling methods.
Method 1: Grouping the town into 8 geographical regions. Then selecting all of the
residents in two randomly selected regions.
Method 2: Grouping the town into 8 geographical regions. Then randomly selecting
residents from each region in proportion to the number of residents in that region.
(c) (i) Write down the name of sampling Method 1 .
(ii) Write down the name of sampling Method 2
(2 marks)
*(d) Give two advantages of using Method 2 rather than Method
(2 marks)

3. (c) Use one word from the list to best complete the statement. Stratified sampling
will help to minimise
(1 mark)

71 | P a g e
4. A large company has 60 offices in different towns. The directors of the company
want to find out the opinions of their employees on a planned change to working
hours. They decide to choose at random 10 offices and survey all the employees in
these offices. (a) State one advantage and one disadvantage of using this sampling
method. (2 marks)

5. Rudra is carrying out an investigation about the amount of money teenagers spend.
He is going to ask 50 teenagers some questions. He asks teenagers going into a
shopping centre until he has asked 25 boys and 25 girls.
(a) Write down the name of this sampling method.
(1 mark)
(b) Give one advantage and one disadvantage of this sampling method.
(2 marks)

72 | P a g e
 ______ / ______ / ______
Capture/Recapture
What is ‘data’ and how can we collect
it?

How can we use the capture/recapture

method for estimating population sizes?
Key Vocabulary
Vocab Mathematical Definition
Everything or everybody that could possibly be involved in an
Population
investigation
Sample A small proportion of the population
A way of estimating the size of a population that cannot be
Capture/Recapture
counted easily

Historical Capture-recapture methods have a long history, and they

Origins were first applied in the study of fish and wildlife
populations before being adapted for other purposes. The
application of these methods to the study of epidemiologic
problems came relatively late in this history and thus has
been able to draw on advances in the other areas as well as
in statistical methods more broadly.

The Knowledge Phase

Some population are easy to count such as the number of students in a school, the
number of products produced at a factory on a particular day, the members at a
tennis club etc.
However, other population can be trickier such as the number of squirrels on the Isle
of Wight, the number of deer at a national park etc.
The capture/recapture method is a way of estimating the size of a population that
cannot be counted easily.
To use the capture/recapture method we need to follow these steps:
1. Assume a population has a total of N
2. Catch M members of the population, tag or mark them
3. Put these members back and allow a little time for the to mix with the population
4. Catch a sample of n members
5. Count how many of this sample are tagged or marked (m)
m M
6. Formulate and solve the equivalent fraction for N =
n N
What must we always assume for this method to be an accurate estimate?

73 | P a g e
 a) The initial sample must have enough time to mix with the rest of the population
b) The initial sample must not have too much time so that the population will have
changed drastically
c) The markings placed on the initial sample must have not come off the sample or
transferred onto the rest of the population

74 | P a g e
I DO

In a wildlife park, 12 rabbits are caught,

marked and released.
A week later 20 rabbits are caught and 1
is found to be marked.
Estimate the number of rabbits in the
park

What assumptions have we made for this

estimate to be accurate?

WE DO

In a lake, 10 fish are caught, marked and

released.
A week later 40 fish are caught and 1 is
found to be marked.
Estimate the number of fish in the lake.

What assumptions have we made for this

estimate to be accurate?

YOU DO

In a safari, 6 wildcats are caught marked

and released.
A week later 10 wildcats are caught and
2 are found to be marked.
Estimated the number of wildcats in the
park.

What assumptions have we made for this

estimate to be accurate?

75 | P a g e
 Practice Questions
1. Peter wants to know how many tigers there are on his nature reserve.
He captures 24 and tags them, then releases them. Two weeks later he
captures 100 tigers and finds that 8 of them are tagged. Estimate how many
tigers are on the reserve.
2. Sahil works for a fish conservation charity and wants to track the decline in fish
in a lake over 10 years. Ten years ago there were approximately 4500 fish in
the lake. This year he catches 100 fish and marks them before throwing them
back in the lake. Two weeks later he captures 100 fish again
and finds that 25 of them have been marked. By what percentage have the
number of fish in the lake declined
3. Helena is running a large table tennis tournament and estimates that she will
need about 1000 table tennis balls for use over the course of the tournament.
Unfortunately, they are all kept in a big barrel in the office and she can’t be
bothered to count them all out to see if she has enough. She picks twenty out
and marks them before throwing them back in and mixing them up thoroughly.
She then picks sixty out of the barrel at random and finds that 2 have been
marked.
a. Should she buy some more table tennis balls for the tournament? If so,
how many?
b. Why does she not need to pick out the first twenty balls at random?
4. Ravi runs a “guess the number of grains of rice in the jar” competition at work
for charity. The following guesses are made:
Harveer: 850 Tom: 312 Dave: 400 Chris: 500
Sophie: 1100 Emily: 750 Samir: 1000
He then takes 40 grains of rice out of the jar and dyes them black. He puts them
back into the jar and shakes them so they are evenly distributed. He takes
another 50 grains out of the jar and finds that 3 of them are dyed black. Who
won the competition?

Exam Questions
1. Richard wants to find an estimate for the number of rabbits living in a section of
woodland. He caught a sample of 25 rabbits, attached a tag to each rabbit, and
then released the 25 rabbits back into the same section of the woodland. Four
weeks later, Richard returned to the same section of woodland and caught a
sample of 10 rabbits. Two of these rabbits were tagged. Using these results,
Richard estimated that there are 125 rabbits in the section of woodland.
a. Show how Richard worked out his estimate of 125 rabbits.
(2 marks)
b. Considering Richard's statistical method, discuss the reliability of his
estimate.
(3 marks)

2. Tania wants to estimate the number of snails in a pond. She takes a sample of
10 snails from the pond. She marks each snail with a waterproof dye and then
76 | P a g e
 puts the snail back in the pond. Two weeks later, Tania takes another sample of
10 snails from the pond. She finds that only one of the snails is marked with the
dye. Tania says, "I estimate there are 100 snails in the pond." How reliable is
Tania's estimate? Give reasons for your answer. You are not required to check
Tania's calculation.
(2 marks)
3. According to an internet site, an estimate of the number of reindeer in a region
of Ontario is 5000 (Source: www.ontario.ca) Giovani wants to verify this
estimate. He goes to the region of Ontario, captures a sample of 250 reindeer,
attaches a tag to each reindeer and then releases the 250 reindeer back into
the same region of Ontario. Three days later, Giovani returns to the same region
of Ontario and catches a sample of 98 reindeer. He finds that 5 of these
reindeer are tagged. Giovani concludes that this information can be used to
verify the estimate of 5000 Discuss the appropriateness of Giovani's method
and of his conclusion. As part of your discussion you should show your
calculations and state any assumptions made.
(5 marks)
4. Margaret and Paul are collecting data on turtles. Margaret wants to estimate the
number of turtles in a lake. She catches a sample of 100 turtles from the lake.
She tags each turtle and then puts them back into the lake. Three days later
Margaret catches 60 turtles from the lake. She finds that 12 of them have been
tagged.
a. Work out an estimate of the total number of turtles in the lake.
(2 marks)
Margaret wants to use this estimate in a report about the turtles in this
lake.
b. How reliable is this estimate? Give reasons for your answer.
(2 marks)
5. A scientist wants to estimate the number of fish in a disused canal. He catches a
sample of 30 fish from the canal. He marks each fish with a dye and then puts
them back in the canal. The next day the scientist catches 20 fish from the
canal. He finds that 4 of them are marked with the dye.
a. Estimate the total number of fish in the canal.
(2 marks)
b. Write down any assumptions you made.
(2 marks)
6. A scientist wants to estimate the number of geese living around a lake. The
scientist captures a sample of 45 geese and puts a tag on each one. He then
releases the geese. The scientist waits one day and captures a sample of 18
geese. He finds that 2 of these geese each have a tag.
a. Estimate the total number of geese living around the lake
(2 marks)
b. Give a statistical reason why the scientist waits one day before taking the
second sample.
77 | P a g e
 The scientist returns to the lake 1 year later and captures a sample of 18
geese. He finds that 1 of these geese has a tag.
(1 mark)
c. Discuss the reliability of using this sample to estimate the total number of
geese now living around the lake.
(2 marks)

78 | P a g e
 ______ / ______ / ______
Questionnaires, Interviews and Pilot Surveys
What is ‘data’ and how can we collect
it?
How do we ensure that a questionnaire is
useful, practical and suitable for an
investigation?
Key Vocabulary
Vocab Mathematical Definition
A way for one person to ask questions and another to answer
Interview
them.
A set of questions that have been written and used to obtain
Questionnaire
data
Open Questions Questions which have no suggested answers
Closed Questions Questions which have suggested answers
Pilot Surveys A trial run of some questions for a questionnaire

Questionnaire: French ‘questionner’ meaning to question

Interview: French ‘s’entrevoir’ meaning to see each other

The Knowledge Phase

Interviews
An interview is a way for one person to ask questions and another to answer them.
This is most often thought of as a face-to-face meeting but it DOES NOT have to be a
face to face conversation. It can also be:
- a phone call
- post or e-mail (similar to a questionnaire)

When choosing the best method for interview techniques there are 5 things we need
to consider:

UNDERSTANDING: think about how we can explain the questions if needs be

CANDOUR: think about what will make the interviewee be more honest

RESOURCES: think about time/costs

INCLUSIVITY: think about how we can ensure everyone responds

INTERVIEWER BIAS: think about the influence of the interviewer

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80 | P a g e
Considering these 5 points, choose the type of interview that is best for each aspect:

Face-to- Phone Email/

Face Call Letter

Understanding

Candour

Resources

Inclusivity

Interviewer Bias

*NOTE* there is no one method if interview that is better than the rest, they all have
their advantages and disadvantages. When choosing the best method the context is
important.

Questionnaires
A questionnaire is a set of questions that have been written and used to obtain data
Questions on a questionnaire come under two categories
Open Questions Closed Questions
These are questions which have no These are questions which have
suggested answers and gives the suggested answer and the responder
responder free reign on how to answer must choose their answer
✓ this can give you ideas of responses
that you wouldn’t have thought of ✓ this gives you data which is easy to
analyse
x this can give you too many varied
responses and make the data too hard
to analyse x the suggested answers may not
exhaust all possibilities or may overlap
and confuse responders

Pilot Survey
To overcome the problem of open questions we can use a pilot survey
A pilot survey is a trial run of some of the possible questions you may want to ask
You ask a smaller sample than you intend to give the questionnaire to
We use them to:
- ask open questions and use responses to create closed question options
- check that the questions make sense to participants

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- help to see if the questions are necessary and the responses are helpful
We then use the responses to help tweak the questionnaire to be used
Criticising Questionnaires – C.O.L.E
C: Choice of Answers
Make sure the question covers all possible options of answers and that they are
clear for all responders
(look at where the options start and finish, are there other possibilities?)

O: Overlapping Boxes
Make sure that the options given to people do not overlap
This is often corrected with the use of inequalities rather than ‘-‘

L: Leading Questions
Make sure that the questions is not sharing the writers opinion and/or asking
responders to
agree/disagree

E: Embarrassing Questions
Questions which are personal may be considered embarrassing to responders and
this can lead to non-
responses or false information
Whilst some questions need to be asked only include persona questions if they are
necessary to the
investigation

I DO

‘How often do you clean your car?’

O never
O once
O 2-5 times
O more than 5 times

Discuss the suitability of this question

WE DO

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 Do you agree that women should not go
out running on their own after work?

O yes
O no

Discuss the suitability of this question

YOU DO

On average, how many pieces of

homework do you get each week?
O none
O 1 – 3 pieces
O 3 – 5 pieces
O 5 or more pieces

Discuss the suitability of this question

Practice Questions
1. George wants to find out how much money people spend on DVDs. He uses this
question.
How much do you spend on DVDs?
O £5 - £10 O £10 - O £30 - O Over
£30 £50 £50
Write down two criticisms of his question.

2. Aidan wants to find out peopleʼs opinion on a new road being built.
A new road will cause a lot of traffic for the village
O Agree O Disagree O Unsure
Write down two things wrong with this question.

3. The manager of a cinema wants to find out how often people go to the cinema.
She uses this question on a questionnaire.
How often do you go to the cinema a month?
O A lot O Often O Many Times
Write down what is wrong about this question.

4. Mrs Jackson wants to find out how much pocket money students are given.
She uses this question.
How much pocket money do you receive a month?

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 O £0 - £5 O £12 - O Over
O £0 - £10 £20 £20
Write down two criticisms of the response boxes.

5. Cameron wants to find out how many televisions people own.

He uses this question in his questionnaire.
How many televisions do you own?
O1–3 O4-6
Write down two different things wrong with this question.

6. Kulwinder uses this question.

What do you think of Chemistry?
O Excellent O Very Good O Good
Write down one thing wrong with this question.

7. Pradeep wants to find out how much time people spend playing sport. He uses
this question on a questionnaire.
How much time do you spend playing sport?
O 0 – 1 hour O 1- 2 hours O 2 – 3 hours
Write down two things wrong with this question.

8. Gordon is going to open a restaurant. He wants to know how often people eat
out at a restaurant.
He designs a questionnaire. He uses this question on a questionnaire.
How often do you go to a restaurant?
O Sometimes O Often O Never
Write down two things that are wrong about this question.

9. Gary wants to find out how much time teenagers spend listening to music.
He uses this question on a questionnaire.
How many hours do you listen to music?
O 1 to 5 O 5 to 10 O 10 to 20 O Over 20
Write down two things wrong with this question.

10. Dave is working for the local MP and trying to gain support based on the
the local transport changes. He asks this question
Do you agree that the bus service has got worse over the last 3 years?
O Yes O No O Unsure
Write down one thing wrong with this question

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Exam Questions
1. A market research company wants to find out whether or not shoppers like a new
shopping centre that has recently opened.
(a) Write down an example of a closed question that could be used on this
questionnaire to find out whether customers like the shopping centre
(2 marks)
It is suggested that a pilot survey is used.
(b) Give two advantages of carrying out a pilot survey.
(2 marks)
One question on the questionnaire is
“Do you agree that the shopping centre is well laid-out and it is easy to find the
goods you want?”
(c) Is this a suitably worded question for the questionnaire? Give reasons for your
answer.
(2 marks)
2. Jenny wants to find out what students at her school think about the after-school
clubs. Jenny is going to use a questionnaire.
Here is one of the questions she wants to put on the questionnaire.

(a) This is not a suitable question. Explain why.

(1 mark)
Here is another of the questions that Jenny wants to put on the questionnaire.

(b) Discuss whether or not this is a suitable question for the questionnaire.
(2 marks)

3. Lian and Natalie own a bookshop. They are investigating the age of each of their
customers and how much each customer spends on books each month. One question
that Lian plans to ask his customers is "How old are you?"
(a) Explain whether or not this is a good question for Lian to ask.
(2 marks)

(b) Write a question that could be used on a questionnaire to find out how much each
customer spends on books each month.
(2 marks)
Natalie thinks that giving a questionnaire to each customer is better than asking the
customers questions face to face.
(c) Give one advantage for each of these methods of collecting data.
(2 marks)

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4. Tracy wants to find out what improvements to the youth club are wanted by the
members of the club. She plans to give each member of the club a questionnaire.
Here is part of the questionnaire.

(a) Explain why Question 2 will not give reliable results.

(1 mark)
(b) Explain why Question 3 is not a good question.
(1 mark)
(c) Explain why there might be a problem with the answers given to Question 4
(1 mark)
(d) Explain why the answers given to Question 5 may not be valid.
(1 mark)

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 ______ / ______ / ______
Cleaning Data
What is ‘data’ and how can we collect
it?

How and why do we ‘clean’ data?

Key Vocabulary

Vocab Mathematical Definition

Facts and information which is collect and presented so it can

Data
be analysed

A method of sorting through data to make it more easily

Cleaning Data
analysable

The Knowledge Phase

When you have some data the first thing you need to do is to check it out and get rid
of any obviously wrong or false data
This is called “Cleaning the Data”

WTLF:
Pointy Pete Silly Samantha
Pete has a problem with the decimal Samantha thinks she's funny
point. She like to write 'funny' answers to
He puts decimals where there shouldn't questions
be one She usually does this on purpose to try
He moves the point around and make everyone's life more awkward
Sometimes he does this on purpose but
most of the time this is an accident

Devious Dave
Obvious Olive Dave is a bit of a trickster
Olive is a little clumsy He messes with the data ON PURPOSE
She makes lots of obvious errors He does it in ways that are not clear to
Sometimes she does this on purpose but see straight away
most of the time its just an accident

I DO
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 Which one of these pieces of data appear
to have been inputted by Pointy Pete?
"How long is your foot in cm?"
3.06 29.5 30.2
28.7 31.4
29.4 29.9 304
Which one of these pieces of data appear
to have been inputted by Obvious Olive?
"What gender to you identify yourself
as?"
Male Female 24
Female Girl
None Boy Male
Which one of these pieces of data appear
to have been inputted by Silly
Samantha?
"Where were you born?"
America Walsall West Brom
England Newquay
The Moon Tipton Wales
Which one of these pieces of data appear
to have been inputted by Devious Dave?
"What is your favourite subject?"
Maths English Spanish
Biology History
P.E Psychology Computing

WE DO
Which one of these pieces of data appear
to have been inputted by Pointy Pete?
"How many minutes dis it take to
complete the puzzle?
3.24 3.95 3.07
0.36 3.24
347 3.45 37.5
Which one of these pieces of data appear
to have been inputted by Obvious Olive?
"What is your favourite flavour ice
cream?"
Chocolate Strawberry Chocolate
Vanilla Yes
Vanilla Chocolate Raspberry
Ripple

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 Which one of these pieces of data appear
to have been inputted by Silly
Samantha?
"How long does it take you to get to
work?"
1hour 45min 30mins
0.5hour 100hours
1.5hour 30mins 30mins
Which one of these pieces of data appear
to have been inputted by Devious Dave?
"How many hours do you spend on social
media per day?"
3 5 8
4 6
1 8 6

YOU DO
Which one of these pieces of data appear
to have been inputted by Pointy Pete?
"How many hours of TV do you watch per
day?"
2.5 4.5 2
0.5 45
2.5 3.5 0.5
Which one of these pieces of data appear
to have been inputted by Obvious Olive?
"What is the highest score you have got
in a maths test?"
56% 12/18 47%
Never 82%
26/28 14/17 94%
Which one of these pieces of data appear
to have been inputted by Silly
Samantha?
"How many packets of crisps do you eat
per week?"
7 5 3
4 50
6 5 2
Which one of these pieces of data appear
to have been inputted by Devious Dave?
"Which spice girl was your favourite?"
Baby Scary Posh
Baby Ginger
Baby Sporty Baby

Other things to look for:

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 - does the data have information missing?
- Does the data need re-writing so that it is all in the same format?

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 Practice Questions

1. Look at the table of data below. Explain how this data should be cleaned before
analysis can take place
Partici 10 11 12
1 2 3 4 5 6 7 8 9
pant
mal girl M F
Sex M F F F M M F F
e
Score 22 24 25 26 23 2.1 21 20 25 29 24 19

2. Look at the data below. Ashleigh believes that the data needs to be cleaned and
that patient C should be removed. Do you agree with her belief?
Patient A B C D E F G H I
Age 32 31 A 25 34 32 36 29 21
Blood
A O 30 B A B O O A
Group

3. Clean the data in the table below and identify which, if any, of the couples
below should be excluded from analysis
Couple a b c d e f G
Before 12.2 15.6 13.7 12.9 14.5 138 19.1
After 10.5 11.7 12.5 10.2 14.9 9.3

4. a) Complete the table below with information from around the room

Male/ School Place of Favourite Transport

Shoe Size
Female Year Birth Subject to School

b) For the data set provided, use highlighters to highlight any information where
cleaning may be necessary
c) Identify which, if any, of the participants you would eliminate
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 5.
Scho Foot
Boy/ Fav Distance
DoB ol Born in Height Lengt
Girl Subject to school
Year h
12.4.2
Boy 5 England 143 26 Art 1-2km
1
31.2.0 Less than
Girl 4 England 132 22 Science
2 2km
14.1.0
Girl 5.00 England 14.2 2.3 PE/Sport 2.5423km
1
Boy 7.9.05 6 England 136 25 Art 1-2km
13.12.
Boy 4 Wales 128 24 PE/Sport 1-2km
01
14.3.1 Less than
Boy 5 England 140 67 PE/Sport
1 1km
Girl 6.5.01 7 Wales 142 24 Art 3-5km
15.8.0
Girl 6 England 138 21 Art 85km
4
20.2.0
Boy 6 England 192 23 PE/Sport 1-2km
2
19.5.9
Girl 6 England 140 20 Maths 1-2km
0
Neith 29.6.0 Planet Going
7 48 21 3000km
er 3 Zog Home
9.10.9 Less than
Boy 4 Scotland 128 21 English
1 1km
18.12. Less than
Girl 5 England 135 21 Geography
02 1km
18.7.0
Girl 0.5 England 13.7 20 Art 3-5km
1
Less than
Boy 3.6.34 4 Wales 129 21 Art
1km
13.2.0
Girl 7 Wales 148 23 Art 1-2km
3
15.9.0
Girl 7 England 150 22.5 PE/Sport 1-2km
4
Less than1
Girl 7.8.03 7 England 140 24 Art
km
Less than
Boy 8.6.03 7 England 142 24 Computing
1km
31.11.
Boy 11 England 1520 22 Computing 5-10km
03
16.7.0
Both 8 Engand 142 26 Japanese 2-3km
4
28.4.0
Girl 8 England 145 26.5 PE/Sport 1 mile
4
Boy 25.3.0 4.1 England 132.1 2.4.5 Maths Less than
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 2 1km
26.2.0 Less than
Boy 4 England 130 21 PE/Sport
2 1km
Girl 8.7.10 6 Waland 142 22 Art 2-3km
23.5.0
Boy 6 England 151 25.5 Maths 2-3km
1
Less than
Boy 1.3.87 9 England 167 25 PE/Sport
1km
Girl 7.8.01 6 England 150 23 History 2 roads
Less than
Girl 3.3.91 4 England 135 21 English
1km

b) For the data set provided, use highlighters to highlight any information where
cleaning may be necessary

c) Identify which, if any, of the participants you would eliminate

Exam Questions
Kerry is investigating whether there is a difference in the lengths of the text messages
sent by boys and sent by girls
at her school.
She writes the following hypothesis for the investigation.
“The length of text messages sent by girls is greater than the length of text
messages sent by boys”.
Kerry decides to use a census of the 800 students in her school. She is going to ask
each student to record the
number of characters in their last text message. Kerry then collects this information
from each student through an
online database.
Part of the database is shown below.
Gender Length of text message
1 male 73
2 F 68
3 girl thirty five
4 boy 114
5 boy 85
6 girl
7 M 56
8 48 boy
9 girl 5
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10 G 75
11 B 41
12 girl 28
Give two reasons why Kerry must clean the data before processing it.
(2 marks)

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 Key words to learn

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 Formulas to learn

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Copyright List
https://corbettmaths.com/wp-content/uploads/2019/01/Primary-
Secondary-Data-pdf.pdf
https://corbettmaths.com/wp-content/uploads/2019/01/Continuous-
Discrete-pdf.pdf
https://corbettmaths.com/wp-content/uploads/2019/01/Qualitative-
Quantitative-Data-pdf.pdf
https://corbettmaths.com/wp-content/uploads/2013/02/types-of-data-
pdf.pdf
https://www.mathsbox.org.uk/re/data/d22/d22checkit.pdf
https://d7dae41c-6434-48e6-a64a-691272fdccba.usrfiles.com/ugd/
d7dae4_13ccc8d2c6624e59aac7883cd55b29cb.pdf
https://d7dae41c-6434-48e6-a64a-691272fdccba.usrfiles.com/ugd/
d7dae4_f28562d5710042e6acef3bc723a53d04.pdf
https://corbettmaths.com/wp-content/uploads/2019/07/Stratified-
Sampling-pdf.pdf
https://d7dae41c-6434-48e6-a64a-691272fdccba.usrfiles.com/ugd/
d7dae4_7854e02029a9472ea722fac474300ca1.pdf
https://corbettmaths.com/wp-content/uploads/2018/10/questionnaires-
pdf1.pdf
https://www.mathsgenie.co.uk/resources/80_questionnaires.pdf
https ://corbettmaths.com/wp-content/uploads/2013/02/random-sampling-
pdf.pdf
https://mathsemporium.com/category/gcse-statistics/2st01-statistics/05-
2st01-past-papers-and-mark-schemes/01-2st01-june-2011/
https://d7dae41c-6434-48e6-a64a-691272fdccba.usrfiles.com/ugd/
d7dae4_7854e02029a9472ea722fac474300ca1.pdf

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